Problem: Simplify the following expression: $ x = \dfrac{5}{8} + \dfrac{y + 1}{y - 6} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{y - 6}{y - 6}$ $ \dfrac{5}{8} \times \dfrac{y - 6}{y - 6} = \dfrac{5y - 30}{8y - 48} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{y + 1}{y - 6} \times \dfrac{8}{8} = \dfrac{8y + 8}{8y - 48} $ Therefore $ x = \dfrac{5y - 30}{8y - 48} + \dfrac{8y + 8}{8y - 48} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{5y - 30 + 8y + 8}{8y - 48} $ $x = \dfrac{13y - 22}{8y - 48}$